Tesla's newly appointed chairwoman Robyn Denholm will bring business expertise to the helm of the company's board and serve as a crucial counterbalance to CEO Elon Musk, even if she isn't the most exciting pick, analysts and experts told CNBC Thursday.

Denholm is the Chief Financial Officer at Australian telecom company Telstra, where she previously served as Chief Operations Officer. She announced Wednesday she was leaving the company and will focus solely on her role as Tesla's chair. Before Telstra, Denholm held executive positions with networking systems companies and served as a national finance manager for Toyota.

Denholm has been on Tesla's board since 2014, which many said is the only real downside to the appointment. Investors and analysts were hoping for a truly independent, outside chairperson to fully check Musk's often wild antics.

It was Musk's controversial tweeting that spurred the SEC fraud charges and subsequent settlement that mandated a new chairperson in the first place.

"I could dream up 10 people from the outside that could be chairperson, but I don't really know, from an ivory tower, if that makes sense," Baird analyst Ben Kallo told CNBC. "We all want a superstar — Larry Ellison at some point, or [Sheryl] Sandberg from Facebook — and as much as that sounds good on paper, in reality this is probably a smarter, more measured decision."

Denholm is as independent as a current insider gets, Kallo said. Among a hand-picked board that includes Elon's brother Kimbal Musk, Denholm is relatively removed. She's also unlikely to make headlines like Musk often does.

"She's always been a voice of good logic and reason [on the board] and helped balance out... anyone that would just go with the flow with Elon," Kallo said. "Can she check Elon? I'm not sure, and I'm not sure if anyone could check him. Maybe his brother, but I think if they had his brother as chairperson everyone would be up in arms."

Tesla still has two more independent directors to appoint in compliance with the SEC settlement. The selections could shed light on Denholm's immediate impact as chairwoman.

"I think what they have to demonstrate is there's a sort of new world order within Tesla — more stringent filters on corporate communications, more objective, well-rounded decisions around corporate governance," Consumer Edge Research analyst Jamie Albertine told CNBC. "I just hope that they're aware of the gravity of the bigger looming question: the broader independence of the board of directors relative to management."

A measured move in the right direction

The lack of fanfare around the selection in and of itself runs counter to Musk's and Tesla's recent volatility. The company's stock saw a period of wild swings, spurred by an Aug. 7 tweet from Musk about taking the company private. Denholm's appointment, by contrast, is almost boring, experts said. The announcement contributed to only modest gains for Tesla on Thursday. The stock was up 1 percent.

"Boring would have been very good on Aug. 7," Albertine said. "I think we need boring, I think we need a more typical, more traditional approach to communications with the market."

The ideal chairperson for a company is often someone who doesn't call attention to themselves, according to John Wilson, head of research and corporate governance at Cornerstone Capital Group.

"It is a hope that she is going to be a counterbalance to the volatility of the CEO, someone who can bring some stable leadership to the board — that would be the best possible outcome," Wilson said. "I would imagine if she's doing her job, you should see a very quick effect."

The job comes with a tall order, though, according to Rohan Williamson, a professor of finance at Georgetown University and expert in corporate governance. Denholm will have to temper some of Musk's "personality" while also shoring up financials for a company that has yet to establish sustainable profitability.

"I think it's a tall ask, because she's doing a little more than typical," Williamson said. "Her background seems to suggest that she should be up to the task."